Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails

Abstract

AbstractWe consider the problem of estimation of the drift parameter of an ergodic Ornstein–Uhlenbeck type process driven by a Lévy process with heavy tails. The process is observed continuously on a long time interval [0, T], $$T\rightarrow \infty $$ T → ∞ . We prove that the statistical model is locally asymptotic mixed normal and the maximum likelihood estimator is asymptotically efficient.